Answer:
The third one, x+(x+1)+(x+2)=-21 because x, x+1 and x+2 are three consecutive numbers.
The greatest number of people that William and Debra may invite and still stay within their budget is 63.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Since William and Debra have budgeted $2,500 for their reception. Therefore, their total expenses should be equal to the total expenses in the reception.
Budget = Total expenses
Budget = Reception hall Cleanup charge + $38 per person fee
Let the number of people invited to the party be represented by x,
$2,500 = $100 + $38(x)
2500 = 100 + 38x
2500 - 100 = 38x
2400 = 38x
x = 2400 / 38
x = 63.157 ≈ 63
Hence, the greatest number of people that William and Debra may invite and still stay within their budget is 63.
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Answer: Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y3" was replaced by "y^3". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(23x2 • y3) - 5
STEP
2
:
Trying to factor as a Difference of Cubes
2.1 Factoring: 8x2y3-5
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 8 is the cube of 2
Check : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result :
8x2y3 - 5
2/5=0.4
5/8=.625
subtract .4 from .625 and get....
.225
and .225 is 9/40
Answer
Correct option is
D
5 cm
△ABC is an equilateral △
∴Area=
4
3
a
2
=75
3
⟹ a
2
=300
a=10
3
cm
AM=MC=
2
10
3
=5
3
cm
Area =
2
1
×AC×BM
75
3
=
2
1
×10
3
×BM
∴BM=15cm
△AOC,△BOC and △AOB are of equal area
∴ar(△AOC)=
3
1
ar(△ABC)=
3
1
×75
3
=25
3
cm
2
In △AOC,
ar(△AOC)=
2
1
×AC×OM
⇒25
3
=
2
1
×10
3
×OM
∴OM=5cm Ans.
